Using plausibility arguments, Mandelstam has shown that the solutions of the Bethe-Salpeter equation in the ladder approximation have branch points in the coupling constant g complex plane. This information is vital for the understanding of the analytic properties and the convergence properties of infinite sums of Feynman diagrams. In this paper we develop a formalism which permits an exact analysis of the coupling constant branch point location for approximate Bethe-Salpeter Pseudopotential equations with nonlocal Pseudopotentials. We apply this formalism to the two-nucleon interaction with the pseudoscalar pion exchange. Exact analytic expressions are found for the g 22/4π branch points which are confirmed by a computer test. The branch point position does not depend either on the pion and nucleon masses, or on the total energy.